Rydberg Formula Calculator

How it works

1/λ = R_∞ · Z² · (1/n₁² − 1/n₂²), R_∞ = 1.0973731 × 10⁷ m⁻¹; series limit: 1/λ = R·Z²/n₁²

Rydberg found in 1888 that every hydrogen line fits one formula with two integers — an empirical pattern Bohr explained 25 years later. Each series shares a lower level: Lyman lines end on n = 1 and lie in the UV, Balmer on n = 2 and span the visible (the four lines you see in a discharge tube), Paschen and beyond are infrared. As n₂ grows the lines crowd toward the series limit, which corresponds to ionising the atom from that level.

Worked example

Balmer n = 4 → 2: 1/λ = 1.097 × 10⁷ × (1/4 − 1/16) = 2.057 × 10⁶ m⁻¹ → λ = 486.1 nm, the blue-green H-β line.

Frequently asked questions